Growth of high quality single crystalline thin films with the use of a temporal seed layer

ABSTRACT

A method of making high quality insulating single crystalline In 2 Se 3  films by (1) depositing at least one quintuple layer (QL) of Bi 2 Se 3  on a substrate layer at a temperature below which only the Se adheres to the substrate; (2) depositing a plurality of In 2 Se 3  QL&#39;s on the deposited Bi 2 Se 3  layer or layers at a temperature between about 200° C. and about 330° C. to form a hetero-structure; and (3) heating the hetero-structure to a temperature between about 400° C. and about 700° C. so that the Bi 2 Se 3  layer is diffused through the In 2 Se 3  layer and evaporated away.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent document claims priority under 35 U.S.C. § 119(e) to theU.S. Provisional Patent Application No. 62/424,943, filed Nov. 21, 2016.This Provisional U.S. Application is incorporated herein by reference inits entirety.

FIELD OF THE INVENTION

This disclosure relates to the field of molecular beam epitaxy (MBE)growth techniques and thin film fabrication of IIIA/VIA and VA/VIAcompounds.

BACKGROUND OF THE INVENTION

It is known that indium selenide (In₂Se₃) possesses at least fivedifferent phases α, β, γ, δ, and κ with a (hexagonal layered structurewith 1.3 eV band gap) and γ (defective wurtzite structure with 2 eV bandgap) being the most stable phases at room temperature. In₂Se₃ offerspromise in applications for optoelectronic devices, non-volatile phasechange memory, and energy storage. Further, due to its similar crystalstructure and small lattice mismatch, In₂Se₃ is a compatible templatefor growth of prototypical 3D topological insulator (TI) Bi₂Se₃. Thisholds great importance since interfacial and bulk defects have remaineda major obstacle for further progress in the field of TIs since theirdiscovery; and thus, having a chemically inert substrate with a smalllattice mismatch is a key step toward suppressing these defects andeventually realization of functional TI devices for application inquantum computation and spintronics.

However, a reliable way to grow high quality single crystalline In₂Se₃,essential for esoteric fundamental physics studies as well as futuretechnology, is still missing. This is because In₂Se₃ grows in apolymorphic fashion on current commercially available substrates, suchas sapphire (Al₂O₃) and strontium titanate (SrTiO₃). Even in the attemptby Rathi et al. “Optimization of In₂Se₃/Si(111) Heteroepitaxy To EnableBi₂Se₃/In₂Se₃ Bilayer Growth” Cryst. Growth Des. 14, 4617-4623 (2014),the MBE growth of In₂Se₃ on H-passivated Si(111), which has a lowerlattice mismatch, led to a disordered interface.

SUMMARY OF THE INVENTION

It has now been discovered that similar to the case of In₂Se₃, which isa proper template for Bi₂Se₃, Bi₂Se₃ can serve as an efficient templatefor In₂Se₃ growth. Exploiting this idea along with growth engineeringtechniques resulted in the growth of single crystalline In₂Se₃ with thehighest so far reported quality.

With the use a temporal seed of Bi₂Se₃, an insulating buffer layer ofIn₂Se₃ with high crystal quality is grown, which, in turn, due tosimilar structure, acts as an efficient template for growth oflow-defect-density Bi₂Se₃, an archetypical 3D topological insulator(TI), with record high mobility. The temporal seed of Bi₂Se₃ initiallyacts as a growth template for the In₂Se₃ layer and then evaporates anddiffuses out of In₂Se₃ layer upon heating to higher temperature leavingbehind only single crystal insulating In₂Se₃ layer. This virtually-grownhigh-quality substrate is an efficient template not only for the Bi₂Se₃layer, but for the entire range of (Bi_(1-x)In_(x))₂Se₃ (0≤x≤1) solidsolution.

Therefore, according to one aspect of the invention, a method of makingan insulating single crystalline In₂Se₃ layer is provided, in which atleast one quintuple layer (QL) of Bi₂Se₃ is deposited on a substratelayer at a temperature below which only the Se adheres to the substrate.A plurality of In₂Se₃ QL's are then deposited on the Bi₂Se₃ layer orlayers at a temperature between about 200° C. and about 330° C. to forma hetero-structure. The hetero-structure is then heated to a temperaturebetween about 400° C. and about 700° C., so that the Bi₂Se₃ layer isdiffused through the In₂Se₃ layer and evaporated away.

In one embodiment, the Bi₂Se₃ is deposited at a temperature betweenabout 110° C. and about 200° C. In another embodiment thehetero-structure is heated to about 600° C. so that the Bi₂Se₃ layer isdiffused through the In₂Se₃ layer and evaporated away.

In one embodiment, the substrate is single crystal Al₂O₃ or a highκ-dielectric SrTiO₃ (111). In another embodiment, a plurality of Bi₂Se₃QL's are deposited on the substrate. In yet another embodiment, at leastone QL of BiInSe₃ is deposited on the In₂Se₃, before the Bi₂Se₃ isdeposited on the BiInSe₃ layer at a temperature below which only the Seadheres to the BiInSe₃ layer.

Stoichiometrically equal quantities of Bi and In in the BiInSe need notbe employed. In one embodiment, at least one QL of Bi₂Se₃ is depositedon said In₂Se₃ layer at a temperature between about 200° C. and about300° C. In one embodiment, the Bi₂Se₃ layer and the BiInSe₃ layer aredeposited at a temperature between about 200° C. and about 300° C.

In one embodiment, a capping layer MoO₃ is deposited on said Bi₂Se₃layer. In another embodiment, an Se layer is deposited on top of theMoO₃ layer.

In another aspect of the present invention, an essentially pure singlecrystal layer of In₂Se on a substrate is provided, prepared by themethod of the present invention. In one embodiment, the substrate issingle crystal Al₂O₃ or a high κ-dielectric SrTiO₃ (111).

In one embodiment, a layer of Bi₂Se₃ is provided on top of said In₂Se₃layer, wherein said Bi₂Se₃ layer has a lattice mismatching less thanabout 1.5%. In yet another embodiment, a layer of BiInSe₃ is providedbetween the In₂Se₃ layer and the Bi₂Se₃ layer.

In another aspect of the present invention, an essentially pure singlecrystal layer of In₂Se₃ on a substrate is provided. In one embodiment, alayer of Bi₂Se₃ is provided on top of said In₂Se₃ layer, wherein saidBi₂Se₃ layer has a lattice mismatching less than about 1.5%. In oneembodiment, a layer of BiInSe₃ is provided between said In₂Se₃ layer andsaid Bi₂Se₃ layer. In one embodiment, the substrate is single crystalAl₂O₃ or a high κ-dielectric SrTiO₃ (111).

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1a illustrates the growth process of In₂Se₃ on Bi₂Se₃ temporallayer with corresponding reflected high-energy electron diffraction(RHEED) at each stage (Adapted from Nano Lett., 15, 8245-8249, 2015).FIG. 1b in comparison, illustrates the growth of In₂Se₃ directly on asapphire substrate which is an indication of lower quality growth.

FIG. 2 shows the Rutherford backscattering spectroscopy (RBS) data andits related fit on a 50 QL Bi₂Se₃ on 10 QL In₂Se₃ heterostructure afterannealing to 600° C. (Adapted from Nano Lett., 15, 8245-8249, 2015).

FIG. 3a illustrates the transmission electron microscopy (TEM) of thebuffer layer which shows the sharp interfaces at each layer. FIG. 3b isa comparison of sheet carrier densities (left panel) and Hall mobilities(right panel) of Bi₂Se₃ films grown on BIS-BL, Al₂O₃(0001) and Si(111)for various film thicknesses (Adapted from Nano Lett., 15, 8245-8249,2015).

FIG. 4a shows the Hall effect (R_(Hall)) as a function of magnetic fieldat various temperatures for an 8 QL thick Bi2Se3 film grown on thebuffer layer; and FIG. 4b shows the longitudinal sheet resistance(R_(sheet)) as a function of magnetic field at various temperatures foran 8 QL thick Bi2Se3 film grown on the buffer layer.

DETAILED DESCRIPTION OF THE INVENTION

The novel growth methodology of high-quality crystalline In₂Se₃ thinfilm and the role of the same as an efficient buffer layer for TI Bi₂Se₃is described in this disclosure. This invention provides a growthprocedure of single crystalline In₂Se₃ using a temporal seed of Bi₂Se₃which can be used for various applications. Moreover, this In₂Se₃ is anexcellent growth template for the entire range of (Bi_(1-x)In_(x))₂Se₃(0≤x≤1) solid solution. More importantly, the growth of Bi₂Se₃ on top ofIn₂Se₃/BiInSe₃ buffer layer resulted in defect-suppressed TI films ofBi₂Se₃ with record low carrier density and high mobility whicheventually revealed novel aspects, such as topological surface states(TSS)-originated quantum Hall effect and quantized Faraday and Kerrrotation which heretofore were unobservable in conventionally grownBi₂Se₃.

The heart of this invention is the temporal seed of Bi₂Se₃ thatinitially acts as a template for the In₂Se₃ layer with any desiredthickness, and then it evaporates away and diffuses out of In₂Se₃ layerupon heating, leaving behind only an insulating In₂Se₃ layer with highcrystallinity. It is worth noting that this growth methodology is notlimited to molecular beam epitaxy (MBE) systems and can be replaced byother growth techniques such as chemical vapor deposition, which ismainly used for industrial applications. Furthermore, this new growthscheme and this highly crystalline buffer layer can be further extendedto the growth of other TI systems, which in turn enhance TI performanceand applicability for the purpose of spintronics and quantum computers.

The method of the present invention includes the following steps:

A single crystal commercially available substrate is prepared. Forexample, an Al₂O₃ (0001) substrate is cleaned ex situ by five minutesexposure to UV-generated ozone and in situ by heating to 750° C. in anoxygen pressure of 1×10⁻⁶ Torr for ten minutes.

99.999% Pure elemental bismuth, indium, and selenium sources areprovided for film growth. For example, the sources are thermallyevaporated using Knudsen cells. As a guide, source fluxes werecalibrated in situ by quartz crystal micro-balance (QCM) and ex situ byRutherford backscattering spectroscopy (RBS). The ratio of selenium fluxto bismuth/indium flux was maintained at above 10:1 as determined byQCM.

Quintuple layers (QL, where 1 QL is made of 5 successive layers ofSe—Bi—Se—Bi—Se and is roughly 1 nm thick) of Bi₂Se₃ are deposited at atemperature at which the atoms will adhere to the substrate, typicallybetween about 110 and about 200° C. to serves as a template for theIn₂Se₃ layer. According to one embodiment, temperature of 135° C. isemployed.

The number of QL is not critical. The Bi₂Se₃ layer can be as thin as 1QL or unlimited in number and thickness. For optimum results in terms ofthe quality of the In₂Se₃ layer grown thereon, at least a 3 QL seedlayer is used.

The thickness of In₂Se₃ deposited on the Bi₂Se₃ layer can be anythingbeyond 1 QL For example, 20 QL In₂Se₃ is deposited on the Bi₂Se₃ layerat a temperature between about 200° C. and about 330° C. In oneembodiment, In₂Se₃ is deposited on the Bi₂Se₃ layer at a temperature orabout 300° C. The 20 QL can be replaced by any other desired thickness.At this point, a hetero-structure is provided consisting of Bi₂Se₃ andIn₂Se₃.

Because of the lower evaporation point of Bi₂Se₃, heating the entirehetero-structure to between about 400° C. and about 700° C. makes theBi₂Se₃ seed layer diffuse through the In₂Se₃ layer and evaporate away,at which point only the QLs of insulating In₂Se₃ remain. In oneembodiment the hetero-structure is heated to about 600° C.

The In₂Se₃ layer is an essentially pure single crystal layer. The singleIn₂Se₃ crystal layer has a purity greater than 99.999%.

Next, a Bi₂Se₃ layer is deposited in the single crystal In₂Se₃ layer. Inone embodiment, solid solution BiInSe₃ of any desired QL thickness isdeposited at a temperature between about 200° C. and about 300° C.,followed by deposition of Bi₂Se₃ within the same temperature range. Inone embodiment, both the BiInSe₃ and the Bi₂Se₃ layers are deposited ata temperature of about 275° C. The combination of single crystallineIn₂Se₃ and BiInSe₃ in the insulating buffer layer (BIS-BL) works as anexcellent template for Bi₂Se₃ growth.

The BiInSe₃ layer minimizes the In diffusion into the top Bi₂Se₃ layer.Moreover, this layer minimizes the lattice mismatching below 1.5%, incomparison to 3%, 14% and 8% lattice mismatch for In₂Se₃, Al₂O₃, and Sisubstrates, respectively, resulting in higher quality growth of Bi₂Se₃.

In addition to Bi₂Se₃, the present invention can also be employed tofabricate thin films of Bi₂Te₃ and Sb₂Te₃.

Essentially any suitable substrate can be used; however, film qualitywill vary depending on the substrate employed. In addition to Al₂O₃substrates, for example, a high κ-dielectric SrTiO₃ (111) substrate canbe employed, which is useful for applying back gate voltage.

SrTiO₃ (STO) substrates are prepared by five minutes ex situ cleaningwith ozone, after which the substrate is heated in situ to about 650° C.and cooled to about 150° C. in an oxygen pressure of 1×10⁻⁶ Torr. Theoxygen helps with further cleaning of the substrate, and concurrently itprevents oxygen deficiencies in STO, thereby maintaining the insulatingproperties.

For STO substrates, the initial QLs of Bi₂Se₃ are deposited at highertemperatures, about 150° C., for example, after which the film is heatedto 300° C. for further deposition of Bi₂Se₃. Thicker films ensure bettertemplates and minimize disorders because Bi₂Se₃ growth on STO substratesis not as good as on Al₂O₃ substrate.

For STO substrates, thin In₂Se₃ (6 QL in one embodiment) is depositedafterward, and the whole hetero-structure is heated to evaporate theunderlying Bi₂Se₃ layer (about 600° C. in one embodiment). This isfollowed by deposition of a thin layer of solid solution BiInSe₃ (3 QLin one embodiment) at about 275° C. in one embodiment.

A top layer of Bi₂Se₃ with any desired thickness is deposited forfurther study and transport measurements. It is better to maintain thislayer as thin as possible for more effective gating. The purpose of thinIn₂Se₃ is to minimize the separation between STO and Bi₂Se₃ and tomaximize the effect of back gating on the Bi₂Se₃ layer.

Finally, for any substrate, a capping layer of electron-depletingmolybdenum oxide (MoO₃) as well as a selenium (Se) layer are depositedin situ on the film. The layers lower the Fermi level and decreasecarrier density even further. They also protect the thin film againstaging in air.

The figures relate to certain embodiments of the invention, in whichFIG. 1a confirms the high-quality 2-dimensional growth of In₂Se₃ ontemporal seeds of Bi₂Se₃. In FIG. 1b , the growth of In₂Se₃ directly ona sapphire substrate is depicted, which is not 2-dimensional, and thestreaks are rather elongated compared to In₂Se₃ growth on Bi₂Se₃.Further, upon rotating the growth stage, the pattern does not rotate orchange in a continuous fashion and instead is static indicating that thesurface is not atomically flat and it has in-plane randomness. This isdue to the polymorphic growth of In₂Se₃ on a sapphire substrate. Thesame thing happens if In₂Se₃ is grown directly on other commerciallyavailable substrates, such as Si and STO.

In FIG. 2, RBS fit to the data gives ˜10 QL thick(Bi_(0.02)In_(0.98))₂Se₃ indicating Bi₂Se₃ evaporates away almostcompletely after annealing the hetero structure to 600° C. The inset isthe cartoon of the film before and after the 600° C. annealing process.The 50 QL thick Bi₂Se₃ is only grown for RBS purpose to demonstrate thateven thick Bi₂Se₃ almost completely evaporates away. In other words, thesmall amount of Bi remained for thick Bi₂Se₃ deposition in FIG. 2becomes completely negligible for the much thinner 3QL Bi₂Se₃ that isused as a template.

The TEM image in the left panel of FIG. 3a shows sharp interfacesbetween Al₂O₃/In₂Se₃, In₂Se₃/BiInSe₃, and BiInSe₃/Bi₂Se₃ layers and theright panel specifically shows the BiInSe₃/Bi₂Se₃ interface clearer.This is an indication of high-quality van der Waals growth at allinterfaces which led to a high quality single crystalline In₂Se₃ layerand eventually low defect density TI thin films with high mobility. Incontrast, TEM images for the interface of In₂Se₃ grown on any commercialsubstrate is quite hazy which indicates disordered growth. The FIG. 3bleft panel compares the sheet carrier density n_(sheet)≈1-3×10¹² cm⁻²for the entire thickness range of 5 to 60 QL Bi₂Se₃ grown on BIS-BL withfilms grown on Al₂O₃(0001) and Si(111) that exhibit an order ofmagnitude larger values of n_(sheet) due to significantly larger defectdensities. The right panel of FIG. 3b shows that the mobility of ˜16,000cm⁻²V⁻¹s⁻¹Bi₂Se₃ grown on BIS-BL is about an order of magnitude largerthan the mobility of films grown on Al₂O₃(0001) and Si(111), and thisdirectly shows that BIS-BL substantially suppresses the net defectdensity.

FIG. 4 depicts the role the atomic-scale virtual substrate In₂Se₃ playsin suppressing the interfacial defects in topological insulator Bi₂Se₃.This led to observation of the quantum Hall effect (QHE) originated fromTSS for the first time in this pure binary compound. FIGS. 4a and 4bshow the Hall effect (R_(Hall)) and the longitudinal sheet resistance(R_(sheet)), respectively, as a function of magnetic field at varioustemperatures for an 8 QL thick Bi₂Se₃ film grown on the buffer layer.The data for 0.3 K shows that R_(sheet) vanishes (0.0±0.5Ω) above 31 Tindicating dissipation-less transport, with simultaneous perfectquantization of R_(Hall)=(1.00000±0.00004)h/e² (25813±1Ω) above 28 T. Asshown in FIGS. 4a and 4b , at the maximum field the quantum Hall plateauvanishes between 20 and 50 K, but the signature of QHE persists even upto 70 K.

Certain embodiments of the invention are depicted by following Examples:

EXAMPLES I. Methods:

Films were grown on 10 mm×10 mm Al₂O₃(0001) substrates usingcustom-built SVTA MOS-V-2 MBE system with a base pressure of 2×10⁻¹⁰Torr. Substrates were cleaned ex situ by five minutes exposure toUV-generated ozone and in situ by heating to 750° C. in an oxygenpressure of 1×10⁻⁶ Torr for ten minutes. 99.999% pure elemental bismuth,indium and selenium sources were thermally evaporated using Knudsencells for film growth. Source fluxes were calibrated in situ by quartzcrystal micro-balance (QCM) and ex situ by Rutherford backscatteringspectroscopy. The ratio of selenium flux to combined bismuth and indiumflux was maintained at above 10:1 as determined by QCM. For 20 QL(Bi_(0.5)In_(0.5))₂Se₃ growth, bismuth and indium were co-evaporated byopening both shutters simultaneously, while the selenium shutter waskept open at all times during growth. For capped films, Se and MoO₃ werethermally evaporated at room temperature for capping.

Films were transferred from the growth chamber to an ex situ cryostatfor transport measurements keeping exposure to less than 5 minutes.Magneto-resistance and the Hall resistance measurements were carried outusing pressed indium leads in van der Pauw geometry in a liquid Hecryogenic system with a base temperature of 1.5 K and in theperpendicular magnetic field (B) up to ±9 Tesla. R_(12,43) (R_(XX)),R_(14,23) (R_(YY)) and R_(13,24) (R_(XY)) were measured using KE2400sourcemeter and KE7001 switch matrix system, where ij are the currentleads and kl are the voltage leads in Rij,kl. R_(XX) and R_(YY) measurelongitudinal resistance, while R_(XY) measures Hall resistance. The datawas symmetrized with respect to B to eliminate unwanted mixing of thelongitudinal and Hall components. From symmetrized R_(XX) and R_(YY),average longitudinal resistance (R_(AVG)) was extracted. The sheetcarrier density was calculated from R_(XY) using the Hall formula:

n _(sheet)=(e dR _(xy) /dB)⁻¹

where dR_(XY)/dB was taken from the linear part of R_(XY) for |B|≤0.5 Tand e is the electronic charge. The carrier mobility (μ) was thencalculated using μ=(e R_(sheet) n_(sheet))⁻¹, where R_(sheet)=R_(AVG)(0)π/ln(2) is the zero field sheet resistance.

For ARPES and STM measurements, the films were capped by a 100 nmselenium over-layer. For STM measurement, ion-milling was performed toremove a few nanometers of ambient contaminated selenium layer followedby annealing to −200° C. to evaporate rest of selenium in the STMchamber. STM measurements were carried out at 78 K using Omicron LT-STMwith a base pressure of 1×10⁻¹¹ Torr. For ARPES measurement, theselenium over-layer was removed by heating the films to ˜250° C. in theARPES chamber. ARPES measurements were then performed at roomtemperature using a 7 eV photon energy LASER source and a SPECS Phoibos225 hemispherical electron analyzer.

TEM samples were prepared by focused ion beam with final Ge ion energyof 5 keV. A JEOL ARM 200CF equipped with a cold field-emission gun anddouble spherical-aberration correctors operated at 200 kV were used forHAADF-STEM image acquisition with a range of detection angles from 68 to280 mrad.

TDMTS measurements were performed in transmission geometry using ahome-built THz detector.

For QHE measurement, an 8 QL thick Bi₂Se₃ film on BIS-BL was grown on 5mm×5 mm Al₂O₃(0001) substrate and in situ capped by both 50 nm MoO₃ and50 nm Se to prevent environmental contamination during transportation tothe National High Magnetic Field Lab in Florida. The film was thenhand-patterned into a Hall-bar just before measurement using a metalmask and a pair of tweezers. Hall and longitudinal resistances weremeasured using a Keithley 2400 source meter combined with a Keithley7001 switch matrix in six-terminal geometry.

II. Evaporation of Bi₂Se₃ Through In₂Se₃ after 600° C. Annealing DuringBIS-BL Growth

In order to study the effect of annealing Bi₂Se₃—In₂Se₃ hetero-structureduring BIS-BL growth, a 50 QL Bi₂Se₃—10 QL In₂Se₃ hetero-structure filmwas grown on Al₂O₃ and annealed it to 600° C. The sample was thenanalyzed using Rutherford backscattering spectroscopy (RBS), which is aquantitative tool to study thickness and composition of thin films. Fromthe total number of each species and known values of the atomic arealnumber density, the film was composed of ˜10 QL (Bi_(0.02)In_(0.98))₂Se₃with 1% error bar in composition. This indicates that the 50 QL Bi₂Se₃layer evaporated away almost entirely leaving behind an intact In₂Se₃layer. This independently confirms the results from HAADF-STEM resultsin FIG. 1b that shows that during the BIS-BL growth, the conducting 3 QLBi₂Se₃ seed layer evaporates almost completely through the 20 QL In₂Se₃layer after 600° C. annealing, thus making the BIS-BL fully insulating.

III. Nonlinear Hall Effect and Two-Carrier Model Fitting

The non-linearity in the Hall Effect was observed at fields higher than˜0.5 T for all films, which usually indicates multiple conductionchannels with different mobilities. Except for 5 QL thick film, whichshows weak non-linearity, all the other films show pronouncednon-linearity similar to 25 and 60 QL thick films. For the non-linearHall effect, the sheet carrier density calculated from low field Hallslope gives a mobility-weighted-average of different carrier speciesrather than carrier density of any single species. In order to specifysheet carrier density and mobility of individual species the two-carriermodel (equation (S1)) was used to fit Hall Effect data:

$\begin{matrix}{{R_{Hall}(B)} = {- {\frac{B}{e}\left\lbrack \frac{\left( {{n_{1}\mu_{1}^{2}} + {n_{2}\mu_{2}^{2}}} \right) + {B^{2}\mu_{1}^{2}{\mu_{2}^{2}\left( {n_{1} + n_{2}} \right)}}}{\left( {{n_{1}\mu_{1}} + {n_{2}\mu_{2}}} \right)^{2} + {B^{2}\mu_{1}^{2}{\mu_{2}^{2}\left( {n_{1} + n_{2}} \right)}^{2}}} \right\rbrack}}} & ({S1})\end{matrix}$

where R_(Hall)(B) is the Hall resistance, B is the applied magneticfield, e is the electronic charge, and n_(i) and μ_(i) are the sheetcarrier density and mobility, respectively, of i^(th) species with i=1,2. n_(i) and μ_(i) are the fitting parameters. Experimentally, there areonly two independent parameters: R_(Hall)(0)/B was fixed to the lowfield slope of the Hall effect, where locally R_(Hall) was linear. Thezero field sheet resistance (R_(sheet))=1/[e(n₁μ₁+n₂/μ₂)] was used toprovide an additional constraint to the fitting. This reduces the numberof independent fitting parameters to just two.

IV. ARPES and Estimate of in Diffusion from STM

One important issue during the growth of Bi₂Se₃ on BIS-BL is thepossibility of indium diffusion into the Bi₂Se₃ film. It is known thatthere can be inter-diffusion between indium and bismuth in Bi₂Se₃ andIn₂Se₃ heterostructures, and the solid solution of (Bi_(1-x)In_(x))₂Se₃goes through a topological phase transition at x≈0.03-0.07, becoming aband insulator for x>0.25. The choice of (Bi_(0.5)In_(0.5))₂Se₃, ratherthan In₂Se₃, as the topmost layer of BIS-BL, helps to minimize indiumdiffusion into Bi₂Se₃ and maintain its non-trivial topology. The TInature of Bi₂Se₃ films grown on BIS-BL even in ultrathin regime is shownby observation of gapped TSS for a 5 QL thick Bi₂Se₃. Such gapped TSShave been observed in ultra-thin Bi₂Se₃ grown on 6H-SiC (0001) with thegap attributed to hybridization of the top and bottom TSS. This isdirect evidence of non-trivial nature of Bi₂Se₃ grown on top of BIS-BLeven in the ultrathin limit. Such an observation means that the Indiffusion should be much less than ˜3%, where a signature of thetopological phase transition starts to appear.

V. Consistency of Transport Data and ARPES with TSS Conduction

From Hall measurement, it is clear that low field sheet carrier density(n_(low)) is less than ˜2×10¹² cm⁻² in the entire thickness range.Two-carrier fitting from the Hall effect measurement gives a total sheetcarrier density (n_(tot)=n₁+n₂) to be at most ˜5×10¹² cm⁻². In Bi₂Se₃,when the total sheet carrier density is ˜1×10¹³ cm⁻² (or equivalently˜5×10¹² cm⁻² per surface) the surface Fermi energy lies at the bottom ofthe bulk conduction band.

Given that the total carrier density n₁+n₂ is much smaller than ˜1×10¹³cm⁻² for films grown on BIS-BL, they should have, if anything, upwardband bending resulting in the formation of a depletion region. Suchupward band bending cannot form quantum well states or 2DEG. Therefore,the most consistent interpretation of the observed channels withthickness independent sheet carrier density is that both of themoriginate from the TSS. This is also supported by ARPES data, where thesurface E_(F) lies in the bulk band gap, and no such 2DEGs are observed.In contrast, ARPES measurements on Bi₂Se₃ grown directly on Al₂O₃clearly show the presence of such 2DEG states. In order to show theexistence of a 2DEG state is unlikely to be present, the expected sheetcarrier density of TSS if either n₁ or n₂ originates from 2DEGs can beestimated. Let us assume that n₁≈1.8×10¹² cm⁻² is due to 2DEG carriers.The Fermi wave-vector for 2DEG using k_(F,2DEG)=√{square root over(2πn₁)} is obtained. This results in k_(F,2DEG)=0.034 Å. Using the ARPESspectrum of Bi₂Se₃ grown on Al₂O₃, the Fermi wave-vector ofcorresponding TSS (k_(F,TSS)) at this k_(F,2DEG) can be extrapolated,which yields k_(F,TSS)≈0.088 Å. From k_(F,TSS), n_(sheet,TSS)=k_(F,TSS)²/4π≈6.1×10¹² cm⁻² for corresponding TSS is calculated, where the 4 inthe denominator is due to the non-degenerate nature of TSS. Similarestimation assuming n₂≈3×10¹² cm⁻² to come from 2DEG yieldsn_(sheet,TSS)≈6.8×10¹², cm⁻². This gives a combined TSS and 2DEG sheetcarrier density of ˜7.9×10¹² cm⁻² (˜9.8×10¹² cm⁻²) from a single surfaceassuming n₁ (n₂) originates from 2DEG state. For simplicity if the othersurface is assumed to have similar carrier density, then the totalcarrier density would be well above ˜10¹³ cm⁻², which is over threetimes that of what is observed from Hall effect which rules out thepresence of 2DEGs. Therefore, it is most natural to associate the twochannels to the TSSs from the top and bottom surfaces, respectively.Naturally, the following question arises: which of the two TSSs isresponsible for the higher mobility channel? This can be indirectlyanswered from the capping layer samples. Considering that the mobilitiesof the Se and MoO₃ capped films are substantially reduced from uncappedsamples, it seems that the higher mobility channel originates from thetop TSS; if the high mobility channel originated from the bottom TSS,such dramatic reduction would not be expected with capping.

The Fermi level (E_(F)) obtained from Hall effect is compared to thatobtained from ARPES on 30 QL Bi₂Se₃ grown on BIS-BL. From ARPES, E_(F)is observed to be ˜0.17 eV above the Dirac point, and the Fermiwave-vector (k_(F)) is observed to be ˜0.052 Å⁻¹. In order to obtainE_(F) from the Hall effect, k_(F,Hall) can be calculated fromk_(F,Hall)=√{square root over (4πn₁)}, wherein n₁ is obtained from atwo-carrier fit of Hall Effect measurement, and the pre-factor 4 is dueto spin non-degenerate nature of TSS. Since n₁ is ˜1.8×10¹² cm⁻² for theentire thickness range, this gives k_(F,Hall) to be ˜0.0475 Å⁻¹.

VI. SdH Oscillation Vs. Cyclotron Resonance

Cyclotron mass can be obtained from Shubnikov-de Haas oscillations inmagnetoresistance measurement or from cyclotron resonance inmagneto-optical measurement. Despite significantly enhanced Hallmobilities, no Shubnikov-de Haas (SdH) oscillations were observed infields up to 9 Tesla. This is surprising considering that the standardBi₂Se₃ or even Cu-doped Bi₂Se₃ films, having much lower mobilitiesexhibit well developed SdH oscillations in fields higher than ˜5 T.Although the origin for the absence of SdH oscillations in these highmobility films is not fully understood yet, one possibility is due tothe carrier density inhomogeneity that may be more severe in these lowcarrier density samples. As previously pointed out in conventional twodimensional electron gas system of similar sheet carrier densities inGaN/AlGaN heterostructures any slight inhomogeneities in the carrierdensity can significantly suppress the SdH oscillation due to the phasecancelling effect: this view is further supported by the veryobservation of the full quantum Hall effect when all carriers are drivento the lowest Landau level, where the effect of any inhomogeneity incarrier densities vanishes. In contrast, well-developed cyclotronresonance was observed in time domain magneto-terahertz spectroscopymeasurement, from which cyclotron mass was extracted.

VII. Time Domain Magneto-Terahertz Spectroscopy Measurement and Fits

In order to measure the complex Faraday rotation (FR), phase modulationtechnique was used to measure the polarization states accurately whichallows measurement of E_(xx)(t) and E_(xy)(t) simultaneously in a singlescan. Faraday rotation can be obtained byθ_(F)=arctan(E_(xy)(ω)/E_(xx)(ω))=θ_(F)′+i θ_(F)″ after Fouriertransforming into the frequency domain. Sapphire has no detectable FRand 20 nm Se or 50 nm MoO₃ do not show rotation within our experimentalaccuracy (0.5 mrad). The non-smooth background from a referencesubstrate was subtracted before fitting the data.

The data were fitted by a Drude-Lorentz model with a Drude term, aphonon term and a term for the background dielectric constant (∈_(∞))coming from higher energy absorptions. The formula for conductance inmagnetic field is

$G_{\pm} = {{- i}\; \epsilon_{0}\omega \; {d\left\lbrack {\frac{\omega_{pD}^{2}}{{- \omega^{2}} - {{i\; \Gamma_{D}\omega} \mp {\omega_{c}\omega}}} + \frac{\omega_{pDL}^{2}}{\omega_{DL}^{2} - \omega^{2} - {{i\; \Gamma_{DL}\omega} \mp {\omega_{cDL}\omega}}} + \epsilon_{\infty} - 1} \right\rbrack}}$

where ω_(p) represents the plasma frequencies, F represents scatteringrates, d is the film thickness, and the ±sign denotes the response toright/left circularly polarized light respectively. The parameters ofthe phonon and the high-frequency terms were constrained by thoseextracted from zero-field conductance value (as explained below) andonly allowed the cyclotron frequency (ω_(n)) and the scattering rate tovary. From G_(±), the complex transmission was calculated for right andleft circularly polarized light t_(±) Then the complex FR was calculatedby tan(θ_(F))=−i(t₊−t⁻)/(t₊+t⁻). From the fits the cyclotron frequency,ω_(c), was extracted for the Drude component from which the cyclotronmass (m*) is calculated using ω_(c)=eB/(2πm*). Similarly, the zero fieldreal conductance spectra was fitted by an oscillator model with a Drudeterm describing free electron-like motion, a Drude-Lorentz term modelingthe phonon and a lattice polarizability (∈_(∞)) term that originatesfrom absorptions outside the spectral range.

${G(\omega)} = {\left\lbrack {{- \frac{\omega_{pD}^{2}}{{i\; \omega} - \Gamma_{D}}} - \frac{i\; {\omega\omega}_{pDL}^{2}}{\omega_{DL}^{2} - \omega^{2} - {i\; {\omega\Gamma}_{DL}}} - {i\left( {\epsilon_{\infty} - 1} \right)}} \right\rbrack \epsilon_{o}d}$

ω_(pD), ω_(p)DL Γ_(DL), and ∈_(∞) obtained from this fit were used toconstrain the fit at finite magnetic field.

These and other advantages of the present disclosure will be apparent tothose skilled in the art from the foregoing specification. Accordingly,it will be recognized by those skilled in the art that changes ormodifications may be made to the above-described embodiments withoutdeparting from the broad inventive concepts of the disclosure. Itshould, therefore, be understood that this disclosure is not limited tothe particular embodiments described herein, but is intended to includeall changes and modifications that are within the scope and spirit ofthe disclosure as defined in the claims.

It will be readily understood that the components of the embodiments asgenerally described herein and illustrated in the appended figures couldbe arranged and designed in a wide variety of different configurations.Thus, the following more detailed description of various embodiments, asrepresented in the figures, is not intended to limit the scope of thepresent disclosure, but is merely representative of various embodiments.While the various aspects of the embodiments are presented in drawings,the drawings are not necessarily drawn to scale unless specificallyindicated.

The present solution may be embodied in other specific forms withoutdeparting from its spirit or essential characteristics. The describedembodiments are to be considered in all respects only as illustrativeand not restrictive. The scope of the present solution is, therefore,indicated by the appended claims rather than by this detaileddescription. All changes which come within the meaning and range ofequivalency of the claims are to be embraced within their scope.

Reference throughout this specification to features, advantages, orsimilar language does not imply that all of the features and advantagesthat may be realized with the present solution should be or are in anysingle embodiment of the invention. Rather, language referring to thefeatures and advantages is understood to mean that a specific feature,advantage, or characteristic described in connection with an embodimentis included in at least one embodiment of the present solution. Thus,discussions of the features and advantages, and similar language,throughout the specification may, but do not necessarily, refer to thesame embodiment.

Furthermore, the described features, advantages and characteristics ofthe present solution may be combined in any suitable manner in one ormore embodiments. One skilled in the relevant art will recognize, inlight of the description herein, that the present solution can bepracticed without one or more of the specific features or advantages ofa particular embodiment. In other instances, additional features andadvantages may be recognized in certain embodiments that may not bepresent in all embodiments of the present solution.

Reference throughout this specification to “one embodiment”, “anembodiment”, or similar language means that a particular feature,structure, or characteristic described in connection with the indicatedembodiment is included in at least one embodiment of the presentsolution. Thus, the phrases “in one embodiment”, “in an embodiment”, andsimilar language throughout this specification may, but do notnecessarily, all refer to the same embodiment.

As used in this document, the singular form “a,” “an,” and “the” includeplural references unless the context clearly dictates otherwise. Unlessdefined otherwise, all technical and scientific terms used herein havethe same meanings as commonly understood by one of ordinary skill in theart. As used in this document, the term “comprising” means “including,but not limited to.”

The term “(s)” following a noun contemplates the singular or pluralform, or both.

The term “and/or” means any one of the items, any combination of theitems, or all of the items with which this term is associated.

The phrases “in one embodiment,” “in various embodiments,” “in someembodiments,” and the like are used repeatedly. Such phrases do notnecessarily refer to the same embodiment, but they may unless thecontext dictates otherwise.

The terms “comprising,” “having,” and “including” are synonymous, unlessthe context dictates otherwise.

The features and functions disclosed above, as well as alternatives, maybe combined into many other different systems or applications. Variouspresently unforeseen or unanticipated alternatives, modifications,variations or improvements may be made by those skilled in the art, eachof which is also intended to be encompassed by the disclosedembodiments.

What is claimed is:
 1. A method of making a high quality singlecrystalline In₂Se₃ layer, comprising: depositing at least one quintuplelayer (QL) of Bi₂Se₃ on a substrate layer at a temperature below whichonly the Se adheres to the substrate; depositing a plurality of In₂Se₃QL's on the deposited Bi₂Se₃ layer or layers at a temperature betweenabout 200° C. and about 330° C. to form a hetero-structure; heating thehetero-structure to a temperature between about 400° C. and about 700°C. so that the Bi₂Se₃ layer is diffused through the In₂Se₃ layer andevaporated away.
 2. The method of claim 1, wherein said Bi₂Se₃ isdeposited at a temperature between about 110° C. and about 200° C. 3.The method of claim 1, wherein said hetero-structure is heated to about600° C. so that the Bi₂Se₃ layer is diffused through the In₂Se₃ layerand evaporated away.
 4. The method of claim 1, wherein said substrate issingle crystal Al₂O₃ or a high κ-dielectric SrTiO₃ (111).
 5. The methodof claim 1, wherein a plurality of Bi₂Se₃ QL's are deposited on saidsubstrate.
 6. The method of claim 1, wherein least one QL of BiInSe₃ isdeposited on said In₂Se₃ layer, after which at least one QL of Bi₂Se₃ isdeposited on said BiInSe₃ layer at the same temperature that BiInSe₃ isgrown on In₂Se₃.
 7. The method of claim 1, further comprising the stepof depositing at least one QL of Bi₂Se₃ on said In₂Se₃ layer at atemperature between about 200° C. and about 300° C.
 8. The method ofclaim 6, wherein said Bi₂Se₃ layer and said BiInSe₃ layer are depositedat a temperature between about 200° C. and about 300° C.
 9. The methodof claim 1, further comprising the step of depositing a capping layerMoO₃ on said Bi₂Se₃ layer.
 10. The method of claim 9, further comprisingdepositing an Se layer on top of said MoO₃ layer.
 11. In combination, anessentially pure single crystal layer of In₂Se₃ on a substrate, preparedby the method of claim
 1. 12. The combination of claim 11, wherein saidsubstrate is single crystal Al₂O₃ or a high κ-dielectric SrTiO₃ (111).13. The combination of claim 11, further comprising a layer of Bi₂Se₃ ontop of said In₂Se₃ layer, wherein said Bi₂Se₃ layer has a latticemismatching less than about 1.5%.
 14. The combination of claim 13,further comprising a layer of BiInSe₃ between said In₂Se₃ layer and saidBi₂Se₃ layer.
 15. In combination, an essentially pure single crystallayer of In₂Se₃ on a substrate.
 16. The combination of claim 15, furthercomprising a layer of Bi₂Se₃ on top of said In₂Se₃ layer, wherein saidBi₂Se₃ layer has a lattice mismatching less than about 1.5%.
 17. Thecombination of claim 16, further comprising a layer of BiInSe₃ betweensaid In₂Se₃ layer and said Bi₂Se₃ layer.
 18. The combination of claim15, wherein said substrate is single crystal Al₂O₃ or a highκ-dielectric SrTiO₃ (111).